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What is the greatest possible area of a triangular region wi

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What is the greatest possible area of a triangular region wi [#permalink] New post   25 Jul 2020, 09:45
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What is the greatest possible area of a triangular region with one side that corresponds with the diameter of a circle with radius 6, and the other vertex of the triangle on the circle?

(A) 24
(B) 36
(C) 40
(D) 48
(E) 72
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Re: What is the greatest possible area of a triangular region wi [#permalink] New post   25 Jul 2020, 11:06
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See the attached image. The key is to place the vertex in such a way that dropping a perpendicular from it will go through the center of the circle. Area is base * height = 36.
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Re: What is the greatest possible area of a triangular region wi [#permalink] New post   26 Jul 2020, 09:13
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Since the base will be same for all such triangles but height will vary, the triangle with maximum area will be the one where the perpendicular dropped from the third vertex on the side coinciding with the diameter passes through the center (the yellow triangle present in the figure).

So,
Max area = (1/2)*(12)*(6) = 36

Answer is B.
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Re: What is the greatest possible area of a triangular region wi [#permalink] New post   20 Aug 2021, 13:30
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since one side is diameter, it's a right triangle
with minimum side, maximum area is attained for square
half of square is 45-45-90 triangle and two legs of triangle must be equal
hence, \(leg=6/\sqrt{2}\) and triangle area is \(\frac{leg^2}{2}\)=\(\frac{36*2}{2}\)=36
answer is B
Carcass wrote:
What is the greatest possible area of a triangular region with one side that corresponds with the diameter of a circle with radius 6, and the other vertex of the triangle on the circle?

(A) 24
(B) 36
(C) 40
(D) 48
(E) 72
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gmatclubot
Re: What is the greatest possible area of a triangular region wi [#permalink]
20 Aug 2021, 13:30
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